A mature oil field is also known as a brown field. Generating schedules of well settings, for example, mid-term (e.g., three years) schedules, for hydrocarbon production in mature oil fields or brown fields is not an easy task. During late stages of an oil field life cycle, oil and gas companies have a tendency to significantly decrease the number of new wells due to low potential return on investments, which may not be sufficient to justify additional capital expenditure. The choice of well control settings (e.g., wellhead choke size at injection wells or frequency of electrical pumps at production wells) in brown fields becomes then a main factor of asset efficiency.
Typically, in order to configure mid-term well settings one uses a set of numerical models to generate forecasts of fluid injection and production at each well as a function of time. Well settings are iteratively adjusted until a given performance metric (e.g., net present value associated with the next three years of production) is improved satisfactorily with respect to an existing baseline, which may correspond to a current schedule of well settings generated heuristically by an expert. Very often in practice, numerical models for production forecast have a relatively large number of parameters (e.g., parameters related to the heterogeneous distributions of rock properties, such as porosity and permeability, in the oil field). These parameters are set so that available information of the field (e.g., history of well production rates) is numerically reproduced. However, the amount of information available is frequently not enough to determine these parameters unequivocally. As a consequence, multiple combinations of model parameters reproduce available information within an acceptable level of accuracy. It should be noticed that these combinations of parameters yield in general different forecasts. The use of only one numerical model can be risky because the attendant prediction can be rather inaccurate. An imprecise prediction can lead to a bad choice of well settings in terms of performance metric. Therefore, the current approach in industry is to consider a set of numerical models (where each model reproduces available information) that provides as a whole an estimation of possible model parameters (since there are multiple models, this estimation will take the form of a collection of values) and allows more robust short-term and mid-term decisions because predictions can be made in a probabilistic manner; e.g., rather than saying that, for example, the field oil production rate after one additional year of production will be of 30,000 bbl/day (if this estimation is determined with only one forecast, the chances that the rate is wrong are, in general, high), one can estimate that the field oil production rate after one additional year of production will be of 25,000 bbl/day with a probability equal to 90% (and this estimation will be, generally, more accurate the higher the number of forecasts that are considered).
Generating a set of numerical models that reproduce available information is usually a time-consuming and complicated process. In order to reproduce available information such as well production and injection rates (which is a type of information commonly considered in most oil fields) physics-based simulations are used to determine how fluids flow in the reservoir. These simulations normally require the solving of computationally expensive systems of nonlinear differential equations. The adjustment of parameters for a single model to reproduce available information is, in general, an iterative process, so several of these time-consuming simulations need to be evaluated until results are deemed acceptable. If, instead of one model, a set of these models is calibrated, the associated computational cost can be prohibitive (e.g., few weeks even on a distributed-computing environment).
The use of few models or models that are not diverse enough or of models that are not geologically plausible may yield to inaccurate forecasts and as a consequence inefficient production of the corresponding oil field. Computing a relatively high number of diverse and geologically realistic models can be a rather time-consuming process and in cases may be prohibitive. Thus, in practice, many state-of-the-art tools for the generation of mid-term schedules of well settings aim at rapid implementations at the expense of forecasts that are based on a set of models that reproduces available information but that is not diverse enough and as a consequence may yield inaccurate predictions.